Question

A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min. for the angle of depression of the car to change from $30^{\circ}$ to $45^{\circ}$ ; then after this, the time taken (in min.) by the car to reach the foot of the tower, is :

• A. $9( 1 +\sqrt{3})$
• B. $18 ( 1 +\sqrt{3})$
• C. $18 ( \sqrt{3} - 1)$
• D. $\frac{9}{2} ( \sqrt{3} - 1)$

Answer 1

Answer: (A)

$9( 1 +\sqrt{3})$

Answer 2

Let length of tower = h $\Rightarrow AC' = AB = h$ and $AC = AB cot 30^{\circ}= \sqrt{3} h$ $\Rightarrow CC' = (\sqrt{3} -1) h$ Time taken by car form C to C' = 18 min $\Rightarrow$ time take by car to reach the foot of the tower = $\frac{18}{\sqrt{3}-1}$ min. = 9 ( $\sqrt{3}$ + 1) min